The count is down to four finalists for the Sarasota county administrator position. County Manager James Baker of York County, S.C.; County Manager Randall Reid of Alachua County, Fla.; Administrator Frederick Russell of Augusta, Ga.; and West Palm Beach, Fla., City Administrator Edward Mitchell have made it to the meet-and-greet round as county leaders work to find a new administrator. A list of nearly 50 candidates was whittled it down to 15 semifinalists last week. Web searches cut that down to nine, and one semifinalist withdrew last week.